%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN143-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:37:09 AM UTC 2026
% Result : Unsatisfiable 1.01s 0.52s
% Output : CNFRefutation 1.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 28
% Syntax : Number of formulae : 94 ( 35 unt; 0 def)
% Number of atoms : 224 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 277 ( 147 ~; 130 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 20 ( 19 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 162 ( 51 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_37,axiom,
n0(b,a),
file('theBenchmark.p',axiom_37) ).
cnf(c_2,plain,
n0(b,a),
inference(clausify,[status(thm)],[axiom_37]) ).
fof(rule_002,axiom,
! [VAR_0,VAR_1] :
( ~ n0(VAR_1,VAR_0)
| l1(VAR_0,VAR_0) ),
file('theBenchmark.p',rule_002) ).
cnf(c_10,plain,
( ~ n0(B,A)
| l1(A,A) ),
inference(clausify,[status(thm)],[rule_002]) ).
fof(rule_066,axiom,
! [VAR_0,VAR_1] :
( ~ n0(VAR_1,VAR_0)
| p1(VAR_0,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_066) ).
cnf(c_17,plain,
( ~ n0(B,A)
| p1(A,A,A) ),
inference(clausify,[status(thm)],[rule_066]) ).
fof(rule_189,axiom,
! [VAR_0] :
( ~ s1(b)
| ~ q2(b,VAR_0,b)
| s2(VAR_0) ),
file('theBenchmark.p',rule_189) ).
cnf(c_78,plain,
( ~ s1(b)
| ~ q2(b,A,b)
| s2(A) ),
inference(clausify,[status(thm)],[rule_189]) ).
fof(rule_273,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ m0(VAR_2,VAR_3,VAR_1)
| ~ s2(VAR_0)
| ~ q2(VAR_2,VAR_0,VAR_2)
| s3(VAR_0,VAR_1) ),
file('theBenchmark.p',rule_273) ).
cnf(c_90,plain,
( ~ m0(C,D,B)
| ~ s2(A)
| ~ q2(C,A,C)
| s3(A,B) ),
inference(clausify,[status(thm)],[rule_273]) ).
fof(rule_279,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ s3(a,VAR_0)
| ~ l2(VAR_2,VAR_1)
| m4(VAR_0,VAR_1) ),
file('theBenchmark.p',rule_279) ).
cnf(c_101,plain,
( ~ s3(a,A)
| ~ l2(C,B)
| m4(A,B) ),
inference(clausify,[status(thm)],[rule_279]) ).
cnf(c_102,plain,
( ~ s1(b)
| ~ q2(b,A,b)
| ~ m0(C,D,B)
| ~ q2(C,A,C)
| s3(A,B) ),
inference(resolve,[status(thm)],[c_90,c_78]) ).
fof(rule_299,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ l1(VAR_0,VAR_2)
| ~ p3(VAR_1,VAR_2,VAR_3)
| s4(VAR_0) ),
file('theBenchmark.p',rule_299) ).
cnf(c_117,plain,
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ),
inference(clausify,[status(thm)],[rule_299]) ).
fof(rule_305,axiom,
! [VAR_0] :
( ~ m4(e,e)
| ~ s4(VAR_0)
| m5(VAR_0,VAR_0) ),
file('theBenchmark.p',rule_305) ).
cnf(c_120,plain,
( ~ m4(e,e)
| ~ s4(A)
| m5(A,A) ),
inference(clausify,[status(thm)],[rule_305]) ).
fof(prove_this,axiom,
~ m5(d,d),
file('theBenchmark.p',prove_this) ).
cnf(c_132,plain,
~ m5(d,d),
inference(clausify,[status(thm)],[prove_this]) ).
cnf(c_136,plain,
( ~ m4(e,e)
| m5(D,D)
| ~ l1(D,B)
| ~ p3(A,B,C) ),
inference(resolve,[status(thm)],[c_117,c_120]) ).
cnf(c_139,plain,
( ~ m4(e,e)
| ~ l1(d,B)
| ~ p3(A,B,C) ),
inference(resolve,[status(thm)],[c_132,c_136]) ).
cnf(c_146,plain,
( ~ l2(E,D)
| m4(C,D)
| ~ s1(b)
| ~ q2(b,a,b)
| ~ m0(A,B,C)
| ~ q2(A,a,A) ),
inference(resolve,[status(thm)],[c_102,c_101]) ).
cnf(c_247,plain,
p1(a,a,a),
inference(resolve,[status(thm)],[c_17,c_2]) ).
cnf(c_267,plain,
l1(a,a),
inference(resolve,[status(thm)],[c_10,c_2]) ).
fof(rule_246,axiom,
! [VAR_0] :
( ~ l2(VAR_0,VAR_0)
| p3(VAR_0,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_246) ).
cnf(c_312,plain,
( ~ l2(A,A)
| p3(A,A,A) ),
inference(clausify,[status(thm)],[rule_246]) ).
fof(rule_182,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ q2(VAR_1,VAR_2,VAR_0)
| ~ n1(VAR_1,VAR_0,VAR_2)
| ~ p1(VAR_0,VAR_0,VAR_2)
| q2(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',rule_182) ).
cnf(c_337,plain,
( ~ q2(B,C,A)
| ~ n1(B,A,C)
| ~ p1(A,A,C)
| q2(A,B,A) ),
inference(clausify,[status(thm)],[rule_182]) ).
fof(rule_181,axiom,
! [VAR_0] :
( ~ p1(VAR_0,VAR_0,VAR_0)
| q2(VAR_0,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_181) ).
cnf(c_338,plain,
( ~ p1(A,A,A)
| q2(A,A,A) ),
inference(clausify,[status(thm)],[rule_181]) ).
fof(rule_177,axiom,
! [VAR_0,VAR_1] :
( ~ p1(VAR_0,VAR_0,VAR_0)
| ~ k0(VAR_1)
| q2(VAR_0,VAR_1,VAR_1) ),
file('theBenchmark.p',rule_177) ).
cnf(c_342,plain,
( ~ p1(A,A,A)
| ~ k0(B)
| q2(A,B,B) ),
inference(clausify,[status(thm)],[rule_177]) ).
fof(rule_133,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ m0(VAR_3,VAR_2,VAR_0)
| ~ s1(VAR_2)
| ~ p0(VAR_1,VAR_1)
| l2(VAR_0,VAR_0) ),
file('theBenchmark.p',rule_133) ).
cnf(c_378,plain,
( ~ m0(D,C,A)
| ~ s1(C)
| ~ p0(B,B)
| l2(A,A) ),
inference(clausify,[status(thm)],[rule_133]) ).
fof(rule_125,axiom,
! [VAR_0] :
( ~ p0(VAR_0,VAR_0)
| s1(VAR_0) ),
file('theBenchmark.p',rule_125) ).
cnf(c_385,plain,
( ~ p0(A,A)
| s1(A) ),
inference(clausify,[status(thm)],[rule_125]) ).
fof(rule_085,axiom,
! [VAR_0,VAR_1] :
( ~ p0(VAR_1,VAR_0)
| p1(VAR_0,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_085) ).
cnf(c_414,plain,
( ~ p0(B,A)
| p1(A,A,A) ),
inference(clausify,[status(thm)],[rule_085]) ).
fof(rule_054,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ n1(VAR_0,VAR_1,VAR_0)
| ~ l1(VAR_2,VAR_0)
| ~ l0(VAR_2)
| n1(VAR_0,VAR_1,VAR_1) ),
file('theBenchmark.p',rule_054) ).
cnf(c_435,plain,
( ~ n1(A,B,A)
| ~ l1(C,A)
| ~ l0(C)
| n1(A,B,B) ),
inference(clausify,[status(thm)],[rule_054]) ).
fof(rule_050,axiom,
! [VAR_0,VAR_1] :
( ~ p0(b,VAR_1)
| ~ l0(VAR_0)
| ~ s0(b)
| n1(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',rule_050) ).
cnf(c_439,plain,
( ~ p0(b,B)
| ~ l0(A)
| ~ s0(b)
| n1(A,B,A) ),
inference(clausify,[status(thm)],[rule_050]) ).
fof(rule_003,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ m0(VAR_1,VAR_0,VAR_2)
| ~ r0(VAR_3)
| ~ p0(VAR_2,VAR_0)
| l1(VAR_0,VAR_1) ),
file('theBenchmark.p',rule_003) ).
cnf(c_477,plain,
( ~ m0(B,A,C)
| ~ r0(D)
| ~ p0(C,A)
| l1(A,B) ),
inference(clausify,[status(thm)],[rule_003]) ).
fof(axiom_32,axiom,
k0(b),
file('theBenchmark.p',axiom_32) ).
cnf(c_482,plain,
k0(b),
inference(clausify,[status(thm)],[axiom_32]) ).
fof(axiom_31,axiom,
m0(b,b,e),
file('theBenchmark.p',axiom_31) ).
cnf(c_483,plain,
m0(b,b,e),
inference(clausify,[status(thm)],[axiom_31]) ).
fof(axiom_23,axiom,
m0(a,e,e),
file('theBenchmark.p',axiom_23) ).
cnf(c_489,plain,
m0(a,e,e),
inference(clausify,[status(thm)],[axiom_23]) ).
fof(axiom_20,axiom,
l0(a),
file('theBenchmark.p',axiom_20) ).
cnf(c_492,plain,
l0(a),
inference(clausify,[status(thm)],[axiom_20]) ).
fof(axiom_19,axiom,
! [VAR_0,VAR_1] : m0(VAR_0,d,VAR_1),
file('theBenchmark.p',axiom_19) ).
cnf(c_493,plain,
m0(A,d,B),
inference(clausify,[status(thm)],[axiom_19]) ).
fof(axiom_14,axiom,
! [VAR_0] : p0(b,VAR_0),
file('theBenchmark.p',axiom_14) ).
cnf(c_497,plain,
p0(b,A),
inference(clausify,[status(thm)],[axiom_14]) ).
fof(axiom_13,axiom,
r0(e),
file('theBenchmark.p',axiom_13) ).
cnf(c_498,plain,
r0(e),
inference(clausify,[status(thm)],[axiom_13]) ).
fof(axiom_12,axiom,
! [VAR_0] : m0(a,VAR_0,a),
file('theBenchmark.p',axiom_12) ).
cnf(c_499,plain,
m0(a,A,a),
inference(clausify,[status(thm)],[axiom_12]) ).
fof(axiom_5,axiom,
s0(b),
file('theBenchmark.p',axiom_5) ).
cnf(c_502,plain,
s0(b),
inference(clausify,[status(thm)],[axiom_5]) ).
cnf(c_1058,plain,
( ~ p0(b,B)
| ~ l0(A)
| n1(A,B,A) ),
inference(resolve,[status(thm)],[c_502,c_439]) ).
cnf(c_599,plain,
( ~ l0(A)
| n1(A,B,A) ),
inference(resolve,[status(thm)],[c_497,c_1058]) ).
cnf(c_634,plain,
( ~ l1(d,E)
| ~ p3(D,E,F)
| ~ l2(C,e)
| ~ s1(b)
| ~ q2(b,a,b)
| ~ m0(A,B,e)
| ~ q2(A,a,A) ),
inference(resolve,[status(thm)],[c_146,c_139]) ).
cnf(c_1059,plain,
( ~ p1(A,A,A)
| q2(A,b,b) ),
inference(resolve,[status(thm)],[c_342,c_482]) ).
cnf(c_745,plain,
q2(a,b,b),
inference(resolve,[status(thm)],[c_1059,c_247]) ).
cnf(c_844,plain,
p1(A,A,A),
inference(resolve,[status(thm)],[c_497,c_414]) ).
cnf(c_849,plain,
s1(b),
inference(resolve,[status(thm)],[c_497,c_385]) ).
cnf(c_861,plain,
q2(A,A,A),
inference(resolve,[status(thm)],[c_844,c_338]) ).
cnf(c_865,plain,
( ~ l1(d,E)
| ~ p3(D,E,F)
| ~ l2(C,e)
| ~ q2(b,a,b)
| ~ m0(A,B,e)
| ~ q2(A,a,A) ),
inference(resolve,[status(thm)],[c_849,c_634]) ).
cnf(c_1060,plain,
( ~ m0(B,A,b)
| ~ r0(C)
| l1(A,B) ),
inference(resolve,[status(thm)],[c_477,c_497]) ).
cnf(c_1061,plain,
( ~ m0(B,A,b)
| l1(A,B) ),
inference(resolve,[status(thm)],[c_1060,c_498]) ).
cnf(c_880,plain,
l1(d,A),
inference(resolve,[status(thm)],[c_1061,c_493]) ).
cnf(c_882,plain,
( ~ p3(D,E,F)
| ~ l2(C,e)
| ~ q2(b,a,b)
| ~ m0(A,B,e)
| ~ q2(A,a,A) ),
inference(resolve,[status(thm)],[c_880,c_865]) ).
cnf(c_920,plain,
n1(a,A,a),
inference(resolve,[status(thm)],[c_599,c_492]) ).
cnf(c_1062,plain,
( ~ m0(C,B,A)
| ~ s1(B)
| l2(A,A) ),
inference(resolve,[status(thm)],[c_378,c_497]) ).
cnf(c_1063,plain,
( ~ m0(B,b,A)
| l2(A,A) ),
inference(resolve,[status(thm)],[c_1062,c_849]) ).
cnf(c_944,plain,
l2(a,a),
inference(resolve,[status(thm)],[c_1063,c_499]) ).
cnf(c_1064,plain,
( ~ m0(C,B,A)
| ~ s1(B)
| l2(A,A) ),
inference(resolve,[status(thm)],[c_378,c_497]) ).
cnf(c_1065,plain,
( ~ m0(B,b,A)
| l2(A,A) ),
inference(resolve,[status(thm)],[c_1064,c_849]) ).
cnf(c_946,plain,
l2(e,e),
inference(resolve,[status(thm)],[c_1065,c_483]) ).
cnf(c_1066,plain,
( ~ p3(B,C,D)
| ~ l2(A,e)
| ~ q2(b,a,b)
| ~ q2(a,a,a) ),
inference(resolve,[status(thm)],[c_882,c_489]) ).
cnf(c_958,plain,
( ~ p3(B,C,D)
| ~ l2(A,e)
| ~ q2(b,a,b) ),
inference(resolve,[status(thm)],[c_861,c_1066]) ).
cnf(c_979,plain,
( ~ l2(B,B)
| ~ l2(A,e)
| ~ q2(b,a,b) ),
inference(resolve,[status(thm)],[c_958,c_312]) ).
cnf(c_996,plain,
( ~ l2(A,e)
| ~ q2(b,a,b) ),
inference(resolve,[status(thm)],[c_944,c_979]) ).
cnf(c_1029,plain,
~ q2(b,a,b),
inference(resolve,[status(thm)],[c_996,c_946]) ).
cnf(c_1030,plain,
( ~ q2(a,A,b)
| ~ n1(a,b,A)
| ~ p1(b,b,A) ),
inference(resolve,[status(thm)],[c_1029,c_337]) ).
cnf(c_1067,plain,
( ~ n1(a,b,a)
| ~ l1(A,a)
| ~ l0(A)
| ~ q2(a,b,b)
| ~ p1(b,b,b) ),
inference(resolve,[status(thm)],[c_1030,c_435]) ).
cnf(c_1068,plain,
( ~ n1(a,b,a)
| ~ l1(A,a)
| ~ l0(A)
| ~ q2(a,b,b) ),
inference(resolve,[status(thm)],[c_844,c_1067]) ).
cnf(c_1069,plain,
( ~ n1(a,b,a)
| ~ l1(A,a)
| ~ l0(A) ),
inference(resolve,[status(thm)],[c_745,c_1068]) ).
cnf(c_1037,plain,
( ~ l1(A,a)
| ~ l0(A) ),
inference(resolve,[status(thm)],[c_920,c_1069]) ).
cnf(c_1070,plain,
~ l0(a),
inference(resolve,[status(thm)],[c_1037,c_267]) ).
cnf(c_1057,plain,
$false,
inference(resolve,[status(thm)],[c_492,c_1070]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN143-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 17:15:16 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 3703317 was started by sandbox on n014,
% 0.08/0.36 % Sat Sep 26 17:15:16 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.37
% 0.12/0.37 % From the command line: assign(max_seconds, 300).
% 1.01/0.52
% 1.01/0.52 % SZS status Unsatisfiable for theBenchmark
% 1.01/0.52
% 1.01/0.52 % Proof 1 at 0.13 (+ 0.02) seconds.
% 1.01/0.52 % Length of proof is 53.
% 1.01/0.52 % Level of proof is 12.
% 1.01/0.52 % Maximum clause weight is 29.000.
% 1.01/0.52 % Given clauses 356.
% 1.01/0.52
% 1.01/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------